The Infinite Impulse Response (IIR) digital filter is well known and widely documented. For a given filter specification, it is known that the sample rate has a significant influence on the required numerical accuracy of the implementation, both in terms of the accuracy of the filter coefficients, and in terms of the precision of the multipliers and adders: the higher the sample rate, the more accuracy is required to maintain the same filter performance. This increases the burden on hardware and software implementations, in turn increasing cost.
In some applications, the signals are intentionally highly over-sampled, meaning that the ratio of the sample rate to highest signal frequency component is high. Although this may at first seem to be inefficient, this does allow a reduction in the number of bits used to represent the signal, and this is often the reason for using over-sampling. For example, it is sometimes appropriate to use only one bit to represent the signal at the over-sampled rate. Thus, there are applications where there are good reasons for an over-sampling situation to exist, and in which it is required to implement an IIR filter. One such example is an ambient noise cancellation system.
There are several standard implementations of the IIR filter, for example the so-called “Direct Form I” and “Direct Form II” types. It is also common to split a higher-order filter into parallel or cascaded second-order sections, or a combination thereof, and there has been much research over the years on the best way to make this subdivision, taking into account stability, fixed-point issues, numerical ranges, and so on. However, all of these architectures suffer from the same numerical accuracy issues when the signals are over-sampled.
The present invention is a method of implementing over-sampled IIR filters without requiring such high numerical accuracy. This leads to a lower cost solution, whether implemented in hardware or software.
Furthermore, it has been found that the feed-forward coefficients of an over-sampled filter are also sensitive to numerical accuracy, and no prior-art method for reducing the computations requirements for this part of the filter has been found. The present invention also includes a method to address this part of the filter.